A complex is represented as `CoCl_(3) . XNH_(3)`. Its `0.1` molal solution in aqueous solution shows `Delta T_(f) = 0.558^(circ). (K_(f)` for `H_(2)O` is `1.86 K "molality"^(-1))` Assuming `100%` ionisation of complex and co-ordination number of `Co` as six, calculate formula of complex.

Options

A. `[Co(NH_(3))_(4)Cl_(2)]Cl`
B. `[Co(NH_(3))_(5)Cl]Cl_(2)`
C. `[Co(NH_(3))_(4)Cl_(2)]Cl`
D. none of these

Answer

To solve the problem, we need to determine the formula of the complex represented as `CoCl₃ . XNH₃`, given the depression in freezing point and the molality of the solution. Here’s a step-by-step solution:

### Step 1: Understand the given data
We are given:
- Depression in freezing point, ΔTf = 0.558 °C
- Kf for water = 1.86 K·kg/mol
- Molality of the solution = 0.1 molal
- Coordination number of Co = 6

### Step 2: Use the formula for depression in freezing point
The formula for depression in freezing point is given by:
\[ \Delta T_f = K_f \cdot m \cdot i \]
where:
- ΔTf = depression in freezing point
- Kf = cryoscopic constant
- m = molality of the solution
- i = van 't Hoff factor (number of particles the solute dissociates into)

### Step 3: Rearranging the formula to find i
We can rearrange the formula to solve for i:
\[ i = \frac{\Delta T_f}{K_f \cdot m} \]

### Step 4: Substitute the known values
Substituting the known values into the equation:
\[ i = \frac{0.558}{1.86 \cdot 0.1} \]

### Step 5: Calculate i
Calculating the right-hand side:
\[ i = \frac{0.558}{0.186} \approx 3 \]

### Step 6: Interpret the value of i
The value of i = 3 indicates that the complex dissociates into 3 particles in solution.

### Step 7: Determine the possible dissociation of the complex
The complex is represented as `CoCl₃ . XNH₃`. Given that the coordination number of Co is 6, we can assume:
- Let’s say it has `X` ammonia (NH₃) ligands.
- The dissociation can be represented as:
- \( \text{Co(NH}_3)_X \text{Cl}_2^+ + \text{Cl}^- \)

### Step 8: Count the ions
From the above dissociation:
- If `X = 5`, then:
- 1 Co complex ion gives 1 Co(NH₃)₅Cl²⁺ and 2 Cl⁻ ions.
- Total = 3 ions (1 + 2 = 3), which matches our calculated i value.

### Step 9: Conclusion
Thus, the formula of the complex is:
\[ \text{CoCl}_2 \cdot \text{NH}_3_5 \]
This indicates that the correct formula for the complex is `CoCl₂(NH₃)₅`.